package h0827;

/**
 * @author 不知名帅哥
 * @version 1.0
 * @description 最小路径和
 * @date 2024/8/27 19:48
 */
public class SmallestPathSum {
    public static void main(String[] args) {
        int[][] grid = {{1, 3, 1}, {1, 5, 1}, {4, 2, 1}};

        int res=getRes(grid);
        System.out.println(res);
    }

    private static int getRes(int[][] grid) {
        //定义dp[i][j]为到达网格i，j的最小路径和
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp=new int[m][n];
        dp[0][0]=grid[0][0];
        //初始化第一行
        for (int i = 1; i < n; i++) {
            dp[0][i] = dp[0][i - 1] + grid[0][i];
        }
        //初始化第一列
        for (int i = 1; i < m; i++) {
            dp[i][0]=dp[i-1][0]+grid[i][0];
        }

        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                //每次都取最小值
                dp[i][j]=Math.min(dp[i-1][j]+grid[i][j],dp[i][j-1]+grid[i][j]);
            }
        }
        return dp[m-1][n-1];
    }
}
